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Greek letters used in mathematics, science, and engineering

Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities. Those Greek letters which have the same form as Latin letters are rarely used: capital Α, Β, Ε, Ζ, Η, Ι, Κ, Μ, Ν, Ο, Ρ, Τ, Υ, and Χ. Small ι, ο and υ are also rarely used, since they closely resemble the Latin letters i, o and u. Sometimes, font variants of Greek letters are used as distinct symbols in mathematics, in particular for ε/ϵ and π/ϖ. The archaic letter digamma (Ϝ/ϝ/ϛ) is sometimes used.

Typography
Some common conventions: • Intensive quantities in physics are usually denoted with minusculeswhile extensive are denoted with capital letters. • Most symbols are written in italics. • Vectors can be denoted in boldface. • Sets of numbers are typically bold or blackboard bold. The Greek letter forms used in mathematics are often different from those used in Greek-language text: they are designed to be used in isolation, not connected to other letters, and some use variant forms which are not normally used in current Greek typography. The OpenType font format has the feature tag "mgrk" ("Mathematical Greek") to identify a glyph as representing a Greek letter to be used in mathematical (as opposed to Greek language) contexts. The table below shows a comparison of Greek letters rendered in TeX and HTML. The lowercase Greek letters used in the TeX rendering is an italic style. This is in line with the convention that variables should be italicized. As Greek letters are more often than not used as variables in mathematical formulas, a Greek letter appearing similar to the TeX rendering is more likely to be encountered in works involving mathematics. Unlike Unicode and HTML, TeX does not have special symbols for Greek capital letters that look identical to their Latin counterparts. Instead the Latin capital letters A, E, Z, H, I, K, M, N, O, P, T, X are used for capital Alpha, Epsilon, Zeta, Eta, Iota, Kappa, Mu, Nu, Omicron, Rho, Tau, and Chi respectively. ==Concepts represented by a Greek letter==
Concepts represented by a Greek letter
Αα (alpha) • \alpha represents: • the first angle in a triangle, opposite the side a • the statistical significance of a result • the false positive rate in statistics ("Type I" error) • the fine-structure constant in physics • the angle of attack of an aircraft • an alpha particle (He2+) • angular acceleration in physics • the linear thermal expansion coefficient • the thermal diffusivity • In organic chemistry the α-carbon is the backbone carbon next to the carbonyl carbon, most often for amino acidsright ascension in astronomy • the brightest star in a constellation • Iron ferrite and numerous phases within materials science • the return in excess of the compensation for the risk borne in investment • the α-conversion in lambda calculus • the independence number of a graph • a placeholder for ordinal numbers in mathematical logic • a type of receptor for the neurotransmitter noradrenaline in neuroscience Ββ (beta) • \Beta represents the beta function • \beta represents: • the thermodynamic beta, equal to (kBT)−1, where kB is the Boltzmann constant and T is the absolute temperature. • the second angle in a triangle, opposite the side b • the standardized regression coefficient for predictor or independent variables in linear regression (unstandardized regression coefficients are represented with the lower-case Latin b, but are often called "betas" as well) • the ratio of collector current to base current in a bipolar junction transistor (BJT) in electronics (current gain) • the false negative rate in statistics ("Type II" error) • the beta coefficient, the non-diversifiable risk, of an asset in mathematical finance • the sideslip angle of an airplane • a beta particle (e− or e+) • the beta brain wave in brain or cognitive sciencesecliptic latitude in astronomy • the ratio of plasma pressure to magnetic pressure in plasma physicsβ-reduction in lambda calculus • the ratio of the velocity of an object to the speed of light as used in the Lorentz factor • a type of receptor for the noradrenaline neurotransmitter in neuroscience Γγ (gamma) • \Gamma represents: • the circulation in fluid dynamics • the reflection coefficient of a transmission or telecommunication line. • the confinement factor of an optical mode in a waveguide • the gamma function, a generalization of the factorial • the upper incomplete gamma function • the modular group, the group of fractional linear transformations • the gamma distribution, a continuous probability distribution defined using the gamma functionsecond-order sensitivity to price in mathematical finance • the Christoffel symbols that describe components of a metric connection • the stack alphabet in the formal definition of a pushdown automaton, or the tape-alphabet in the formal definition of a Turing machine • the Feferman–Schütte ordinal Γ0 • atmospheric lapse rates in meteorology • \gamma represents: • the specific weight of substances • the lower incomplete gamma function • the third angle in a triangle, opposite the side c • the Euler–Mascheroni constant in mathematics • gamma rays and the photon • the heat capacity ratio in thermodynamics • the Lorentz factor in special relativity • the flight path angle of an airplane Δδ (delta) • \Delta represents: • a finite difference • a difference operator • a symmetric difference • the Laplace operator • giving heat in a chemical reaction • the angle that subtends the arc of a circular curve in surveying • the maximum degree of any vertex in a given graphsensitivity to price in mathematical finance • the discriminant of a polynomial (in a quadratic polynomial determines the nature of the roots) • \delta represents: • percent error • a variation in the calculus of variations • the Kronecker delta function • the Feigenbaum constants • the force of interest in mathematical finance • the Dirac delta function • the receptor which enkephalins have the highest affinity for in pharmacology • the Skorokhod integral in Malliavin calculus, a subfield of stochastic analysis • the minimum degree of any vertex in a given graph • a partial charge. δ− represents a negative partial charge, and δ+ represents a positive partial charge in chemistry(See also: Solvation) • the chemical shift of an atomic nucleus in NMR spectroscopy. For protons, this is relative to tetramethylsilane = 0 • stable isotope compositionsdeclination in astronomy • in set theory, the limit ordinal of the sequence \omega,\omega^{\omega},\omega^{\omega^{\omega}},\dots • in computer science, the empty string • the Levi-Civita symbol • in electromagnetics, dielectric permittivityemissivitystrain in continuum mechanicspermittivity • the Earth's axial tilt in astronomyelasticity in economicselectromotive force • in chemistry, the molar extinction coefficient of a chromophore • in mathematics, a surreal number that is bigger than zero, but smaller than all positive real numbers. • set membership symbol ∈ is based on ε (digamma) • is sometimes used to represent the digamma function, though the Latin letter F (which is nearly identical) is usually substituted. • A hypothetical particle Ϝ speculated to be implicated in the 750 GeV diphoton excess, now known to be simply a statistical anomaly Ζζ (zeta) • \zeta represents: • the Riemann zeta function and other zeta functions in mathematics • the damping ratio • the value for the Zeta potential, i.e., the electrical potential at the slipping plane, used often in colloidal chemistry Ηη (eta) • \Eta represents: • the Eta function of Ludwig Boltzmann's H-theorem ("Eta" theorem), in statistical mechanicsInformation theoretic (Shannon) entropy • \eta represents: • the intrinsic wave impedance of a medium (e.g. the impedance of free space) • the partial regression coefficient in statistics, also interpreted as an effect size measure for analyses of variance • the eta mesonviscosityenergy conversion efficiencyefficiency (physics) • the Minkowski metric tensor in relativity • η-conversion in lambda calculus • the learning rate in machine learning and statistics • the hapticity of a coordination complex ligand Θθ (theta) • \Theta (uppercase) represents: • an asymptotically tight bound related to big O notation. • sensitivity to the passage of time in mathematical finance • in set theory, a certain ordinal numberHeaviside step function • \theta (lowercase) represents: • a plane angle in geometry • the angle to the x axis in the xy-plane in spherical or cylindrical coordinates (mathematics) • the angle to the z axis in spherical coordinates (physics) • the potential temperature in thermodynamics • theta functions • the angle of a scattered photon during a Compton scattering interaction • the angular displacement of a particle rotating about an axis • the Watterson estimator in population genetics • the thermal resistance between two bodies • \vartheta ("script theta"), the cursive form of theta, often used in handwriting, represents • the first Chebyshev function in number theoryTheta role in linguistics Ιι (iota) • \iota represents: • an inclusion map in set theory • the index generator function in APL (in the form ⍳) • the interior product Κκ (kappa) • \Kappa represents: • the Kappa number, indicating lignin content in pulp • \kappa represents: • the Von Kármán constant, describing the velocity profile of turbulent flow • the kappa curve, a two-dimensional algebraic curve • the condition number of a matrix in numerical analysis • the connectivity of a graph in graph theorycurvaturedielectric constant (\varepsilon / \varepsilon_0) • thermal conductivity (usually a lowercase Latin k) • electrical conductivity of a solution • thermal diffusivity • a spring constant (usually a lowercase Latin k) • the heat capacity ratio in thermodynamics (usually \gamma) • the receptor which dynorphins have the highest affinity for in pharmacology Λλ (lambda) • \Lambda represents: • the Lebesgue constant, a bound for the interpolation error • the von Mangoldt function in number theory • the set of logical axioms in the axiomatic method of logical deduction in first-order logic • the cosmological constant • the lambda baryon • a diagonal matrix of eigenvalues in linear algebra • a latticemolar conductivity in electrochemistry • Iwasawa algebra • \lambda represents: • one wavelength of electromagnetic radiation • the decay constant in radioactivity Μμ (mu) • \mu represents: • the Möbius function in number theory • the population mean or expected value in probability and statistics • a measure in measure theorymicro-, an SI prefix denoting 10−6 (one millionth) • Micrometre or micron (retired in 1967 as a standalone symbol, replaced by "μm" using the standard SI meaning) • the coefficient of friction in physics • the service rate in queueing theory • the dynamic viscosity in physics • magnetic permeability in electromagnetics • a muonreduced mass • the ion mobility in plasma physics • the Standard gravitational parameter in celestial mechanicspopulation mean in statisticschemical potential in thermodynamicsAbsorption coefficientAmplification factorMagnetic moment of a dipoledegrees of freedom in statistics • the matching number of a graph • the p-adic valuation of a number Ξξ (xi) • \Xi represents: • the original Riemann Xi function, i.e. Riemann's lower case ξ, as denoted by Edmund Landau and currently • the xi baryon • \xi represents: • the original Riemann Xi function • the modified definition of Riemann xi function, as denoted by Edmund Landau • the extent of reaction Οο (omicron) • \Omicron represents: • O (for "Ordnung") in Donald Knuth's reading of the big O notation Ππ (pi) • \Pi represents: • the product operator in mathematics • a plane • the unary projection operation in relational algebra • the Pi function, i.e. the Gamma function when offset to coincide with the factorial • the complete elliptic integral of the third kind • the fundamental groupoidosmotic pressure • \pi represents: • Archimedes' constant (more commonly just called Pi), the ratio of a circle's circumference to its diameter • the prime-counting function • the state distribution of a Markov chain • in reinforcement learning, a policy function defining how a software agent behaves for each possible state of its environment • a type of covalent bond in chemistry (pi bond) • a pion (pi meson) in particle physics • in statistics, the population proportionnucleotide diversity in molecular genetics • in electronics, a special type of small-signal model is referred to as a hybrid-pi model • in discrete mathematics, a permutationProjectionparallax in astronomy • \varpi (a graphic variant, see pomega) represents: • angular frequency of a wave, in fluid dynamics (angular frequency is usually represented by \omega but this may be confused with vorticity in a fluid dynamics context) • longitude of pericenter, in astronomycomoving distance, in cosmology • the lemniscate constant Ρρ (rho) • \Rho represents: • one of the Gegenbauer functions in analytic number theory (may be replaced by the capital form of the Latin letter P). • \rho represents: • one of the Gegenbauer functions in analytic number theory. • the Dickman–de Bruijn function • the radius in a polar, cylindrical, or spherical coordinate system • the correlation coefficient in statistics • the radius of convergence in real analysis • the sensitivity to interest rate in mathematical financedensity (mass or charge per unit volume; may be replaced by the capital form of the Latin letter D) • one Turn (angle) measured in radians • Kendall tau rank correlation coefficient, a measure of rank correlation in statistics • Ramanujan's tau function in number theoryshear stress in continuum mechanics ϒυ (upsilon) • \Upsilon (U+03D2) represents: • the upsilon meson Φφ (phi) • \Phi represents: • the work function in physics; the energy required by a photon to remove an electron from the surface of a metal • magnetic flux or electric flux • the cumulative distribution function of the normal distribution in statistics • phenyl functional group in organic chemistry (pseudoelement symbol) • the reciprocal of the golden ratio (represented by \phi, below), also represented as 1/\phi • the value of the integration of information in a system (based on integrated information theory) • Geopotential • Alternative symbol for a wave function in quantum mechanics Note: The empty set symbol ∅ looks similar, but is unrelated to the Greek letter. • \phi or \varphi represents: • the golden ratio 1.618... in mathematics, art, and architecture • Euler's totient function in number theory • the argument of a complex number in mathematics • the value of a plane angle in physics and mathematics • the angle to the z axis in spherical coordinates (mathematics) • epoch or phase difference between two waves or vectors • the angle to the x axis in the xy-plane in spherical or cylindrical coordinates (physics) • latitude in geodesyradiant fluxneutron fluxPotential energyelectric potential • a scalar field in quantum field theory • the probability density function of the normal distribution in statistics • the Veblen functions Χχ (chi) • \chi represents: • the chi distribution in statistics (\chi^2 is the more frequently encountered chi-squared distribution) • the chromatic number of a graph in graph theory • the Euler characteristic in algebraic topologyelectronegativity in the periodic table • the Fourier transform of a linear response function • a character in mathematics; especially a Dirichlet character in number theory • sometimes the mole fraction • a characteristic or indicator function in mathematics • the magnetic susceptibility of a material in physics • the fission neutron energy spectrum in neutron transport Ψψ (psi) • \Psi represents: • a quaternary combinator in combinatory logic • a symbol for psychology • the wave function in the Schrödinger equation of quantum mechanics • the second Chebyshev function in number theory • the polygamma function in mathematicsthe supergolden ratio • In circadian physiology, ψ represents the phase relationship between a zeitgeber and a biological rhythm. • In virology the ψ site is a viral packaging signal. • Water potential in movement of water between plant cells. Ωω (omega) • \Omega represents: • Absolute infinite • the SI unit measure of electrical resistance, the ohm • an asymptotic lower bound notation related to big O notation • in probability theory and statistical mechanics, the support • a solid angle • the first uncountable ordinal (also written as ω1) • Chaitin's constant for a given computer program • the vacuum state in quantum field theory • \omega represents: • angular velocity / radian frequency (rad/sec) • the symbol ϖ, a graphic variant of π, is sometimes construed as omega with a bar over it; see π • the unsaturated fats nomenclature in biochemistry (e.g. ω−3 fatty acids) • the first uncountable ordinal \omega_1 (also written as Ω) • the clique number (number of vertices in a maximum clique) of a graph in graph theory == See also ==
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